Introduction

Abstract

The representation theory of finite groups is a subject going back to the late eighteen hundreds. The pioneers in the subject were G. Frobenius, I. Schur, and W. Burnside. Modern approaches tend to make heavy use of module theory and the Wedderburn theory of semisimple algebras. But the original approach, which nowadays can be thought of as via discrete Fourier analysis, is much more easily accessible and can be presented, for instance, in an undergraduate course. The aim of this text is to exposit the essential ingredients of the representation theory of finite groups over the complex numbers assuming only knowledge of linear algebra and undergraduate group theory, and perhaps a minimal familiarity with ring theory.